On $(n-1)$-bicolorable Steiner triple systems of order $2^n-7$

Source abstract

A Steiner triple system STS of order $v$ is a hypergraph of rank 3, with $v$ vertices and such that every 2-subset of vertices has degree 1. In this paper we construct STS$(2v+7)$ containing subsystems STS of order $v$. This construction allows us to obtain, for any $n\ge 5$, $(n-1)$-bicolorable systems STS$(2^n-7)$ having a maximal independent set of largest cardinality. Received: 04 May 2026 | Accepted: 18 June 2026